Sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving η-semidifferentiable type I-preinvex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type I-preinvex and related functions. Our result generalize the results of Preda [V. Preda, ...

This paper presents a fuzzy goal programming FGP procedure for solving bilevel multiobjective linear fractional programming BL-MOLFP problems. It makes an extension work of Moitra and Pal 2002 and Pal et al. 2003 . In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers DMs objective functions at both levels as well as the membership functions for ...

*Correspondence: [email protected] Chung-Jen Junior College of Nursing, Health Sciences and Management, Dalin, 62241, Taiwan Abstract In this paper, we establish sufficient optimality conditions for the (weak) efficiency to multiobjective fractional programming problems involving generalized (F,α,ρ ,d)-V-type I functions. Using the optimality conditions, we also investigate a parametric-type dua...

⎯The convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a type I and related functions. Sufficient optimality conditions are established under the aforesaid assumptions. Several duality theorems are obtained for Wolfe type and Mond-Weir type duals and the original problem. Keyword⎯Minimax programming; Fractional programming; Sufficient...

In this paper we present a review of the main theoretical results obtained up to now in bicriterion fractional programming with few exceptions related to general results for bicriteria problems. With respect to sequential methods, we limit ourselves to present computational approaches for linear fractional problems.

For 1 1 ( ) ( )∈! m m m x = x ,...,x , y = y ,...,y we put ≤ x y iff i i x y ≤ for each { } 1 2 ∈ i M = , ,...,m ; ≤ x y iff ≤ i i x y for each i M ∈ , with x y; x < y ≠ iff i i x < y for each i M ∈ . We write + ∈! m x iff 0 ≥ x . For an arbitrary vector n x∈! and a subset J of the index set { } 1 2 n , ,..., , we denote by J x the vector with components j x , j J ∈ . Let ( ) μ X , Γ, be a fini...